@techreport{138c8a9df6c54b9e8ef35b396e2c2c60, title = "On a Galois property of fields generated by the torsion of an abelian variety", abstract = " In this article, we study a certain Galois property of subextensions of $k(A_{\mathrm{tors}})$, the minimal field of definition of all torsion points of an abelian variety $A$ defined over a number field $k$. Concretely, we show that each subfield of $k(A_{\mathrm{tors}})$ which is Galois over $k$ (of possibly infinite degree) and whose Galois group has finite exponent is contained in an abelian extension of some finite extension of $k$. As an immediate corollary of this result and a theorem of Bombieri and Zannier, we deduce that each such field has the Northcott property, i.e. does not contain any infinite set of algebraic numbers of bounded height. ", keywords = "math.NT, 11J95, 11R32", author = "Sara Checcoli and Dill, {Gabriel A.}", note = "16 pages, added Section 4 on the validity of the main result over other ground fields, comments are welcome", year = "2023", month = jul, day = "31", language = "French", type = "WorkingPaper", }